On the depth of randomly generated circuits

  • Tatsuie Tsukiji
  • Fatos Xhafa
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1136)


This research is motivated by the Circuit Value Problem; this problem is well known to be inherently sequential. We consider Boolean circuits with descriptions length d that consist of gates with a fixed fan-in f and a constant number of inputs. Assuming uniform distribution of descriptions, we show that such a circuit has expected depth O(log d). This improves on the best known result. More precisely, we prove for circuits of size n their depth is asymptotically ef ln n with extremely high probability.Our proof uses the coupling technique to bound circuit depth from above and below by those of two alternative discrete time processes. We are able to establish the result by embedding the processes in suitable continuous time branching processes. As a simple consequence of our result we obtain that monotone CVP is in the class average NC.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Tatsuie Tsukiji
    • 1
  • Fatos Xhafa
    • 2
  1. 1.Dept. of Computer ScienceTokyo Institute of TechnologyTokyoJapan
  2. 2.Dept. of LSI Faculty of InformaticsUPCBarcelonaSpain

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